A Stochastic Approach to Hotel Revenue Management Considering Individual and Group Customers

Transcription

1 Proceedngs of the Internatonal Conference on Industral Engneerng and Operatons Management Bal, Indonesa, January 7 9, A Stochastc Approach to Hotel Revenue Management Consderng Indvdual and Group Customers M. A. Vahdat, Sh. Golestany, M. H. Abooe and M. Honarvar Department of Industral Engneerng Yazd Unversty Yazd, Iran Abstract hs paper develops a stochastc model for capacty allocaton wth robust optmzaton n the quantty-based revenue management. hs model consders customers arrval both ndvdually and n group, lmted tme horzon and capacty. he polcy s to provde early dount durng a determned deadlne n the bookng perod n order to provoke demand. hs model determnes the optmal bookng lmts for each class of customers by usng a two-stage stochastc programmng n order to control nventory durng bookng perod. It can be used for optmzaton of hotel revenue management system, also as a gude for decson makers n developng ther own polces for acceptng or not acceptng bookng requests for the hotel. Keywords Capacty allocaton, Hotel revenue management, Robust optmzaton, Stochastc programmng.. Introducton Revenue management s the art of maxmzng proft generatng from a lmted capacty of a product, over a fnte horzon, by sellng each product to the rght customer wth the rght prce at the rght tme (ercyanl 9). hs approach has developed from ts orgn, the arlne ndustry, to ts current poston, as one of the most mportant busness actvtes n a wde range of ndustres, ncludng hosptalty, energy, retal, and manufacturng (Subramanan et al. 999). hs approach has ntegrated marketng as well as fnancal and operatonal actvtes to maxmze revenue from current capacty (Crystal 7). Dependng on the decsons made to manage demand, revenue management s dvded nto quantty-based or prced-based revenue management. In quantty-based approach, the problem of rejecton or acceptance of an order, and the capacty allocaton to dfferent classes of customers are expressed, whle prced-based approach expresses the problem of determnng the prce of dfferent product types or the product prce over tme. Some ndustres may use the combnaton of prce-based and quanttybased revenue management. Among quantty-based decsons, the ones related to capacty allocaton and nventory control, allow managers to look for optmal balance between customer demand and the systems ablty to provde servces that meet the demand. Revenue management, n the hotel ndustry, s a selecton process, n whch the acceptance or rejecton of customers s based on the prce rates, arrval date, and the length of stay n order to maxmze revenue. hs s done by matchng the avalable facltes wth customer demands to get the most proft by combnng customers. he man purpose of ths study s to present a mathematcal programmng model for the optmzaton step n applyng revenue management n hotels. he model s also an approprate capacty allocaton and nventory control. hs study s an attempt to develop a practcal model based on the lterature n ths area. It also famlarzes the reader wth the operatonal envronment and the exstng stuaton of reservaton. In ths study the model of determnng the bookng lmt and the optmal allocaton were obtaned by usng a two-stage stochastc programmng wth regard to arrval of customers s ndvdual or group, lmted tme horzon and capacty. In ths model, the early dount strategy for ndvdual customers has been added and two prce classes for two bookng perods were also consdered. he paper s organzed as follows: secton derbes the notatons, parameters and assumptons of the model. he basc stochastc programmng model for hotel revenue management s presented n Secton. In Secton, stochastc programmng model wth robust optmzaton s developed. A numercal llustratve example s presented n secton 5. Fnally, n Secton 6, conclusons and recommendatons for future research are dussed. 7

2 . Mathematcal Modelng Before presentng stochastc programmng model, ths secton ntroduces the assumptons, notatons, parameters and varables of the model... Model Assumptons In the presented model, plannng s done for a perod of days. No customer s n hotel before the frst day () and all customers have left the hotel by end of perod. Mnmum resdng s one nght. Customers arrve ndvdually or n groups and the hotel provde only one class of rooms. In ths model, the early dount strategy has been consdered. Customers can reserve rooms wth lower prce n a certan tme perod. wo classes of prce are consdered, normal prce wth bookng lmt Bl and dount prce wth bookng lmt Bl. wo bookng perods are also consdered, the frst tme perod, offerng early dount, thus, t s possble to book wth two dfferent rates: dount prce and normal prce. Bookng wth dount prce s not allowed to cancel and the change must be pad fully n advance; but bookng wth normal prce s allowed to cancel before startng the perod. In the second tme perod, bookng s only possble wth the normal prce. If part of the related capacty to dount prce s not sold out n the pror perod, t could be sold wth a normal prce n the second perod. In addton, the possblty to change bookng class has been consdered for customers. If the demand for class, n the frst perod, s more than ts related capacty, the model gves chance to the customer to take the other opton. Wth respect to operatonal envronment and stochastc demand, there are dfferent enaros for demand wth a certan probablty on each day of the perod. Dfferent demand enaros can have dfferent or the same prces. he possblty of cancelng the bookng s also consdered n the model... Notatons and Defntons : he arrval day n the consdered perod, (=,,,-) j: he check-out day n the consdered perod, (j=,,,) m: Prce class, (m=,) g: Group number, (g=,,) k: he consdered day (k=,,,-) : Length of the consdered perod, (=,,,) : he set of dfferent demand enaros, (=,,,Sc).. Parameters C: total capacty P m : Sellng prce for ndvdual bookng to class m p': Sellng prce for group bookng S g : he sze of group g for check-n on day and check-out on day j U m : bookng demand for check-n on day and check-out on day j n class m q : Probablty of acceptance of normal prce by class customer e m : Probablty of cancelaton for class m S g: he sze of group g for check-n on day and check-out on day j under Scenaro U m: bookng demand for check-n on day and check-out on day j n class m under Scenaro M: he upper range for L pr : Probablty of occurrence of enaro λ: Rsk averson W m : Penalty for the devaton of certan demand for class m on day w' : : Penalty for the devaton of certan demand for group customers on day D. Decson Varables Bl m :Bookng lmt for sellng capacty to class m on day Blg : Bookng lmt for sellng capacty to group customers on day x m : he number of bookng capacty of class m for check-n on day and check-out on day j y g : he probablty of acceptance of group g for check-n on day and check-out on day j x m: he number of bookng capacty of class m for check-n on day and check-out on day j under Scenaro y g: he probablty of acceptance of group g for check-n on day and check-out on day j under Scenaro 7

3 . Problem Formulaton he basc mathematcal programmng model s presented as follows. G Max Z = j p x j p s y () s.t. m m g g m j g j k G k e x y s C k=,,...,- () m m g g m jk g jk G e x y s C () m jm jg jg m j g j x U =,...,- j=,..., () x U Max, U x * q =,...,- j=,..., (5) xm,yg, x s nteger. m he objectve functon () seeks to maxmze revenue and t has two parts. he frst part shows revenue from capacty allocaton to ndvdual customer and the second part shows revenue from group customers. Constrant () ensures that the number of customers on day k do not exceed the maxmum capacty of the hotel. In ths constrant, the lkelhood of cancellaton has been consdered and assumed that the probablty of cancellaton by customer class m s e m ; so ths assumpton has been used n the capacty constrants. Constrant () lmts the number of customers arrval to the maxmum capacty on day zero. wo constrants () and (5) ensure the number of admtted customers for check-n on day and check out on day j are not more than expected demand. Constrant (5) has been added demand of class, to expected demand of class, f capacty related to class has been sold out. Because constrant (5) s nonlnear, the above model s converted to the followng lnear model wth some modfcatons on the constrant: x U h * q =,...,- j=,..., (6) L =U x =,...,- j=,..., (7) L -h +M M =,...,- j=,..., (8) -L +h =,...,- j=,..., (9) h M =,...,- j=,..., () -L +h +M M =,...,- j=,..., () L -h =,...,- j=,..., () 7

4 xm, h,yg,, =, x m s nteger. L s free. In the above constrants h s equal to Max, U Bl and takes zero or L; f L s negatve t takes zero.. Stochastc Programmng Model and Robust Optmzaton Uncertanty s a key element n many decson-makng problems. Fnancal plannng, arlnes plannng, and hedulng are the examples of areas that gnorng may lead to errors n decson-makngs. here are often varous ways n whch uncertanty can be formulated and several approaches have been developed for optmzng under uncertanty over recent years. In tradtonal methods, senstvty analyss approaches are used to consder the uncertanty of the data. In such approaches, professonals and model desgners gnore the effect of the uncertanty of the data at frst and subsequently use senstvty analyss to endorse the obtaned results. However, senstvty analyss s the only tool to analyze the answers. It cannot be used to produce robust answers. In addton, the use of senstvty analyss n the models that have a large number of uncertan data s not practcal. Another approach that has been recently developed to cope wth uncertanty n data s robust optmzaton. hs approach seeks solutons close to optmum that are feasble wth hgh probablty. In other words, by gnorng the objectve functon, the possblty of answers obtaned wll be ensured. Here, a unque approach based on probablstc uncertanty models s consdered. By consderng the average of feasble outcomes or possblty of occurrence of events, objectves and constrants of the correspondng mathematcal programmng model can be defned. In the real world, uncertanty has not been consdered n many models or f used t usually leads to nonlnear and complex models that cannot be optmzed. he am of ths study s to present capacty allocaton n revenue management for uncertan data that have an acceptable performance. he desgned stochastc programmng and robust optmzaton model s presented below: Max Z = - Sc Sc G pr j pm x m pr j p sg y g m j g j Sc G Sc Sc G pr j pm x m j p sg y g pr j pm x m pr j p sg y g m j g j m j g j - +max, q s.t. Sc g pr w U U x Bl w U Bl w sg B j j g j k G k m m g g m jk g jk G emx jm y jgsjg C m j g j j G x m lg () e x y s C k=,,...,- =,...,Sc () =,...,Sc (5) Bl m m=, =,,...,- =,...,Sc (6) y s Bl g =,,...,- =,...,Sc (7) g g g j U x =,...,- j=,..., =,...,Sc (8) x U +max, U x q =,...,- j=,..., =,...,Sc (9) Bl max U =,,...,- =,...,Sc () j 7

5 Bl max U + max U Bl q =,,...,- =,...,Sc () j j g Blg max sg =,,...,- =,...,Sc () g j x, B l C, Blg C, y,, =, x,b l, Blg are nteger. m m g m m he frst two terms, n the objectve functon, represent revenue from servcng to customers; the next statement shows the mean absolute devaton from the average revenue for dfferent enaros. λ s a non-negatve weghtng parameter that s brought as a rsk averson factor; the more the rate of management rsk, the smaller the value of ths coeffcent wll be. If the dfference of revenue from varous enaros be hgh, the amount of penaltes wll ncrease, too. hus, the model seeks to mnmze ths dfference. In hs method, the objectve functon looks for maxmzng soluton robustness. he next term represents the devaton of the varous demand enaros and w, w' are non-negatve weghtng parameters that s used as penalty for devaton from the specfc demand. hus, the objectve functon seeks to maxmze model robustness. Wth regard to the presented model whch s non-lnear, the theory devsed by Yu and L () can be used to lnearze t. By usng the proposed theory, our stochastc model s also converted to lnear form. he non-negatve varables k k and k were presented for the set of enaros and the model wth the changes n the objectve functon and addng some constrant comes n the form below. Sc Sc G Z pr jpmxm pr jp sg y g m j g j Sc G Sc Sc G pr j pm x m j p sg y g pr j pm x m pr j p sg y g m j g j m j g j Max = - Sc g - pr w U h * q Bl w U Bl w sg B lg j j g j () s.t. k G k e x y s C k=,,...,- =,...,Sc () m m g g m jk g jk G emx jm y jgsjg C m j g j j G x =,...,Sc (5) m Bl m m=, =,,...,- =,...,Sc (6) y s Bl g =,,...,- =,...,Sc (7) g g g j U x =,...,- j=,..., =,...,Sc (8) x U + h * q =,...,- j=,..., =,...,Sc (9) L = U x =,...,- j=,..., =,...,Sc () L -M =,...,- j=,..., =,...,Sc () h -M =,...,- j=,..., =,...,Sc () -L -M =,...,- j=,..., =,...,Sc () -L +M h M =,...,- j=,..., =,...,Sc () L h =,...,- j=,..., =,...,Sc (5) 75

6 Bl max U =,,...,- =,...,Sc (6) j Bl max U + max U Bl q =,,...,- =,...,Sc (7) j j g Blg max sg =,,...,- =,...,Sc (8) g j Sc Sc G G pr jpmxm pr jp sg y g jpmxm jp sg y g m j g j m j g j Bl =,...,Sc (9) U =,...,- =,...,Sc () j j Bl U h * q =,...,- =,...,Sc () g sg g j B lg =,...,- =,...,Sc () x, B l C, B lg C, h, y,, =, x,b l, B lg,h are nteger. L s free. m m g m m 5. Illustratve Example In ths secton we consder a numercal example n order to carry on a prelmnary test of the extended model. We assume a case where a hotel would lke to take four dfferent demand enaros nto ts plannng wth the probablty of occurrence.,.,.5 and.5, respectvely. he prces per resdng nght for ndvdual customers are.8 and.69 (normal prce and dount prce) and t s.65 for group customers. he total capacty of hotel s 5. he plannng horzon s set to be 5 days. he rsk averson factor s equal to. he demands are shown as the followng tables and for the four enaros. In each enaro, each row represents a customer's arrval day and each column represents the check-out day and the class of customer for the reservaton. For example, number 8 n the frst row of the frst enaro, column., shows the customer demand of class for check-n on day and check-out on day. Smlarly, able shows the sze of the customer of group g for check-n on day and check-out on day j. able : Demands for ndvdual customers (U m) Scenaro Scenaro Scenaro Scenaro able : Demands for group customers (S g) Scenaro

7 able contnued: Demands for group customers (S g) Scenaro Scenaro Scenaro Scenaro Frst stage able : Optmal soluton Frst stage Indvdual Class customers' 86 bookng Class lmt 7 6 Group customers' bookng lmt X m able : Optmal soluton Second stage (Indvdual) X m X m X m

8 he optmal frst stage solutons obtaned are then summarzed n ables -5; Namely, the bookng lmt for each class of customers, ndvdual customers and group customers, for each arrval day. For example, the bookng lmt on day for class s and for class s 6; also acceptng group customers s optmal. able shows the optmal allocaton for the arrval day and the check-out day and customer's class n the event any of the enaros. he value of the varable y g for days that are equal to n table 5, ths means the acceptance of group customers on these days. able 5: Optmal soluton Second stage (groups) y g y g y g Conclusons and Future Study Hotel ndustry has provded a necessary platform for the mplementaton of revenue management approach to manage the demand and maxmze the revenue. In ths paper, a mathematcal programmng model has been developed n context of capacty allocaton and nventory control, for applcatons n ths ndustry. hs model, amng to maxmze revenue, determnes the bookng lmts for each class of customers (ndvdual and group) and also specfes the amount of allocated capacty to each class accordng to the check-n and check-out date. In ths model customers arrval s assumed as ndvdual and group and a specfc polcy s also consdered to offer early dount for ndvdual customer f booked before a certan date. It s possble to change the bookng class when the dounted prce class s sold out. Because of the specal characterstcs of the operatng envronment and unspecfed demand, the stochastc model under varous enaros was developed and robust optmzaton approach wth mnmzng the devaton from the average revenue and the devaton from demand for dfferent enaros was used to n order to provde solutons close to the optmum that are feasble wth hgh probablty. In the presented model, n order to avod the loss of potental proft caused by room cancellaton, a lmted overbookng s added to the model. In ths case, there s always a rsk that passengers may arrve more than the avalable capacty. In these cases the hotel has to provde another place whch s usually n hgher class. herefore, a hgh penalty for bookng cancellaton should be consdered n the model to mnmze the overbookng costs. hs s stated as a suggeston for future research. References Badnell.R.D,, "heory and Methodology, An optmal, dynamc polcy for hotel yeld management", European Journal of Operatonal Research, Vol., PP Ben-al. A., El Ghaou. L., Nemrovsk. A., 9, "Robust Optmzaton", Prnceton Unversty Press. Btran.G.R, Mondhen.S.V, 99, "An Applcaton of Yeld Management to the Hotel Industry", Btran.G.R, Glbert.S.M, 996, "Managng hotel reservatons wth uncertan arrvals", Operatons Research, Vol, No, PP Chan ao Hung,, "Revenue Management of Hotel Industry n Hong Kong", hess, Cty Unversty of Hong Kong. Crystal.C.R, 7, "Revenue Management Performance Drvers: An Emprcal Analyss n the Hotel Industry", Dssertaton, School of Georga ech College of Management, Georga Insttute of echnology. El Gayar. N., Zakhary. A., Abdel Azz. H., Saleh. M., Atya. A., El Shshny. H.,, "An Integrated Framework for Advanced Hotel Revenue Management", Internatonal Journal of Contemporary Hosptalty Management, Vol., No., PP y g

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